During playing I was desperately looking for a reason to call river while instinct was to fold.
But more careful examination is in order to see the ranges. I recall my opponent being reasonable and not cold calling a lot on preflop. I didn't have a lot of hands so there is some margin of error.
This is how I imagine his cold call range:
99-22, AQs-A7s, KTs+, QTs+, JTs, T9s, AQo-ATo, KQo (148 hands)
Some of those hands may go into a 3bet some of those may be folded. I think some discounts on KTs, QTs, AQs are in order for that reason.
Question 1
Is it a good continuation bet on such a board assuming I do not have a hand? On this flop there are 132 hands.
The answer may depend on whether I hold ace of hearts.
AhQh-Ah7h, KTs+, QJs, QTs, JTs, KQo, ATo, 55 will not fold T9s, AQ, AJ may not fold as well. Worst case scenario: there is resistance with 81 hand which brings us to 37.9% fold equity. Bet of my size requires 41.6% fold chance therefore it is not enough. Discounts and likely folds of AQ and AJ make this bet barely profitable. if opponent cold calls preflop with QJo bluff bet flop is misplaced.
Now lets assume that I hold ace of hearts: that leaves 67 hands out of 118 hands for resistance which brings us to 43% fold chance on worst case scenario. And this is assuming out opponent never raises flop with complete garbage.
Summary:
continuation bet will be unprofitable or barely profitable
having ace of hearts in hand makes bet better
Question 2
Suppose I made continuation bet on flop. Should I bet turn?
Assume worse: AhQh-Ah7h, KTs+, QJs, QTs, JTs, KQo, ATo, 55 resisted
Note that we should discount 55 and KT because it is very likely that our opponent will raise flop for defense. We may need to discount some flush draws as well since opponent may raise flop. At this point there are 3 possible sets, I will leave 2. And I will leave only 1 KTs. I will put Ah7h, AhQh on raise flop as well that leaves us with
55 (2), KTs (1), Ah8h, Ah9h, AhJh, AT (12), KQo (12), JTs(3), QJs(4) 37 total.
Resistance is expected from 55, KTs, KQo, QhJh, AhJh (17) for sure.
Possibly Ah8h, Ah9h, QJs (3)
Unlikely AT
If there was a call with QJo then that as well. Overall it seems that bluff bet on turn is actually good.
Now onto river and the actual hand.
We can expect our opponent to have 55(2), KTs(1), busted draws (AhJh, Ah9h, Ah8h) are discounted since I have ace of hearts, QJs (1-4) may still be here, KQo(9)
55 and QJ are stronger, KTs is weaker, KQo will not call therefore I should not make that river bet.
Hand proved to be more interesting than I initially thought, I will put it into hand evaluation after all.